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An explicit solution to the Skorokhod embedding problem for double exponential increments

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  • Nguyen, Giang T.
  • Peralta, Oscar

Abstract

Strong approximations of uniform transport processes to the standard Brownian motion rely on the Skorokhod embedding of random walk with centered double exponential increments. In this note we make such an embedding explicit by means of a Poissonian scheme, which both simplifies classic constructions of strong approximations of uniform transport processes (Griego, 1971) and improves their rate of strong convergence (Gorostiza and Griego, 1980). We finalize by providing an extension regarding the embedding of a random walk with asymmetric double exponential increments.

Suggested Citation

  • Nguyen, Giang T. & Peralta, Oscar, 2020. "An explicit solution to the Skorokhod embedding problem for double exponential increments," Statistics & Probability Letters, Elsevier, vol. 165(C).
    • Handle: RePEc:eee:stapro:v:165:y:2020:i:c:s016771522030170x
    DOI: 10.1016/j.spl.2020.108867
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    References listed on IDEAS

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    1. Guy Latouche & Matthieu Simon, 2018. "Markov-Modulated Brownian Motion with Temporary Change of Regime at Level Zero," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1199-1222, December.
    2. Garzón, J. & Gorostiza, L.G. & León, J.A., 2009. "A strong uniform approximation of fractional Brownian motion by means of transport processes," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3435-3452, October.
    3. Albrecher, Hansjörg & Ivanovs, Jevgenijs, 2017. "Strikingly simple identities relating exit problems for Lévy processes under continuous and Poisson observations," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 643-656.
    4. Gábor Horváth & Miklós Telek, 2017. "Matrix-analytic solution of infinite, finite and level-dependent second-order fluid models," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 325-343, December.
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